Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.

Permutations - dCode

Tag(s) : Combinatorics

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⮞ Go to: Rank of a Permutation

Tool to generate permutations of items. In Mathematics, a permutation is an arrangement of distinct items in various orders 123,132,213,231,312,321.

Item **permutations** consist in the list of all possible arrangements and ordering of elements in any order.

__Example:__ The three letters A,B,C can be shuffled (anagrams) in 6 ways: A,B,C B,A,C C,A,B A,C,B B,C,A C,B,A

**Permutations** should not be confused with combinations (for which the order has no influence) or with arrangements also called partial **permutations** (k-permutations of some elements).

The best-known method is the Heap algorithm (method used by this dCode's calculator).

Step 1 - for each item, fix it at the beginning

Step 2 - repeat step 1 with the remaining items

**Permutations** can thus be represented as a tree of **permutations**:

Counting **permutations** uses combinatorics and factorials

__Example:__ For $ n $ items, the number of **permutations** is equal to $ n! $ (factorial of $ n $)

Having a repeated item involves a division of the number of **permutations** by the number of **permutations** of these repeated items.

__Example:__ DCODE 5 letters have $ 5! = 120 $ **permutations** but contain the letter D twice (these $ 2 $ letters D have $ 2! $ **permutations**), so divide the total number of **permutations** $ 5! $ by $ 2! $: $ 5!/2!=60 $ distinct **permutations**.

**Permutations** makes exponential values which needs huge computing servers with huge memory cells, so the generation must be paid.

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Source : https://www.dcode.fr/permutations-generator

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